Drawing on in-depth interviews with 50 Latin American immigrants in Dallas, Texas, this article uncovers systematic distinctions in how immigrants holding a range of legal statuses perceive the threat of deportation. Undocumented immigrants in this study recognize the precarity of their legal status, but they sometimes feel their existence off the radar of the U.S. immigration regime promotes their long-term presence in the country. Meanwhile, documented immigrants in this study describe the relative stability of their legal status, but they sometimes view their existence on the radar of the U.S. immigration regime as disadvantageous to their long-term presence in the country. To explain these perspectives, the article develops the concept of “system embeddedness” to denote individuals’ perceived legibility to institutions that maintain formal records. System embeddedness is one mechanism through which perceived visibility to the U.S. immigration regime entails risk, and perceived invisibility safety, for some immigrants. In this way, the punitive character of the U.S. immigration regime can overwhelm its integrative functions, chilling immigrants out of opportunities for material and social well-being through legalization and legal status in ways that likely have intergenerational consequences. More broadly, system embeddedness illuminates how perceived legibility to a record-keeping body combining punitive and integrative goals—even absent punitive experiences with other systems of social control—represents a mechanism of legal stratification for subordinated populations.